Frequentist methods in addressing the piecewise constant signal de-noising problem include penalization methods like the fused lasso method [1]} and the \(L_1\) -fusion method [2]}. The Bayesian equivalent of the fused lasso penalty is using a Laplace shrinkage prior on the successive differences \(\eta \)  [3]}. However, the Laplace prior leads to posterior inconsistency [4]}. To overcome this problem, [5]} used a heavy-tailed shrinkage prior for the coefficients in a linear regression framework. Motivated by this, [6]} proposed to use a \(t\) -shrinkage prior for Bayesian fusion estimation. [7]} use a Normal Exponential Gamma (NEG) prior in this context, and make inference based on the posterior mode.
